Page 748 - Engineering Digital Design

714 CHAPTER 14/ASYNCHRONOUS STATE MACHINE DESIGN AND ANALYSIS

Indirect Path (IP) Requirements for E-hazard and D-trio Formation The first-order
IP requirements are as follows:

1. The IP must not be inconsistent with the conditions of the initiating state a in
Fig. 14.27a, including its state variables and all input conditions other than the initiator
input.
2. The IP must contain the initiator as Xj or x t•.
3. The IP must follow a path to the RG that is unobstructed. Thus, IP terms in the second
invariant function Yj must not be inconsistent with any input held constant.

With reference to Fig. 14.27a, the IP must not be inconsistent with •••)>/,)'_/••• , Xj and
must contain *, or f, in Yj.
A SIMPLE EXAMPLE. Consider the state diagram for the simple two-input FSM shown
in Fig. 14.28a. Here, two paths are shown, one for an E-hazard and the other for a d-trio.
The shaded states indicate the origin states for the potential defect in question. Thus, the E-
hazard path is c —> b —> a while that for the d-trio isa-+d-+c-+das indicated by the
dashed arrows. Notice that there are no endless cycles or critical races present in this FSM.
So that the reader can follow the reasoning process involved in analyzing these potential
defects, the NS functions, read from the K-maps in Fig. 14.28b, are provided in Eqs. (14.20)
and (14.21) and are used for E-hazard and d-trio analysis, respectively. In these equations
RG represents a race gate or a path to a race gate, and IP represents an indirect path term. The

Path of ABO in V^ C n< IDA Path of
d-trio ^^v/ X V^*-^ E-hazard

(b)

FIGURE 14.28
E-hazard and d-trio analysis for a simple FSM having two inputs and one unconditional output,
(a) State diagram showing paths for an E-hazard and for a d-trio. (b) NS K-maps and minimum cover.